SOLUTION: through(4,5); parallel to the x-axis

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Question 760513: through(4,5); parallel to the x-axis
Answer by MathLover1(20855) About Me  (Show Source):
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Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is 0 (its from the slope of y=0%2Ax%2B0 which is also 0). Also since the unknown line goes through (4,5), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-5=0%2A%28x-4%29 Plug in m=0, x%5B1%5D=4, and y%5B1%5D=5



y-5=0%2Ax-%280%29%284%29 Distribute 0



y-5=0%2Ax-0 Multiply



y=0%2Ax-0%2B5Add 5 to both sides to isolate y

y=0%2Ax%2B5 Combine like terms

So the equation of the line that is parallel to y=0%2Ax%2B0 and goes through (4,5) is y=0%2Ax%2B5


So here are the graphs of the equations y=0%2Ax%2B0 and y=0%2Ax%2B5



graph of the given equation y=0%2Ax%2B0 (red) and graph of the line y=0%2Ax%2B5(green) that is parallel to the given graph and goes through (4,5)